Question

A cat sees a mouse in front of him
Ran to catch. At the same time the cat is 4 times and the rat is 6 times
Jump the bar. But the cat jumped 7 times that distance
The rat crossed that distance by jumping 5 times. Ratio of speed of cat and rat​

Answer 1

Given :

The no of jumps by cat is 8 and by mouse is 6 in same interval of time .

Distance covered by cat in 7 jumps is equal to that by mouse in 5 jumps .

To Find :

Ratio of speeds of cat and mouse = ?

Solution :

Let the given same interval of time be t .

So, time taken by cat for 1 jump = $\frac{8}{t}$

And , time taken by mouse for 1 jump = $\frac{6}{t}$

Let the equal distance covered be = x

So, the time taken by cat to cover x in 7 jumps = $\frac{7 \times 8}{t}$

$=\frac{56}{t}$

And the time taken by mouse to cover x in 5 jumps $= \frac{5 \times 6}{t}$

$= \frac{30}{t}$

So , the speed of cat = $\frac{x}{\frac{56}{t}} = \frac{xt}{56}$

And speed of mouse = $\frac{x}{\frac{30}{t}} = \frac{xt}{30}$

So, the ratio of speeds :

$=\frac{(\frac{xt}{56})}{(\frac{xt}{30})}$

$=\frac{30}{56}$

$=\frac{15}{28}$

Hence , ratio of their speeds is 15 : 28